I fully agree and have been advocating for the introduction of traits/protocols/concepts or some such thing in Julia. But the problem is not that Base is untyped in the current type system, it's that the type system is not expressive enough to talk about the information you want to talk about.

Map should have type

  map(f : T -> U, arr : Iterable{T}) -> Iterable{U}

None of that can be expressed in the Julia type system as is. There is no AbstractCallable type that functions would be subtypes of, and there is no Iterable trait (AbstractArray comes closest but without multiple inheritance of AbstractTypes you can not rely on it).